If a body loses half of it's velocity on penetrating a 4 cm wooden block , how much more will it penetrate before coming to rest?

Let's assume the initial velocity of the body is V and it penetrates the wooden block by x cm before coming to rest.

According to the question, the body loses half of its velocity on penetrating the wooden block. This means the final velocity of the body after penetrating the block is V/2.

Using the equation of motion:

v^2 = u^2 + 2as

Where:
v = final velocity
u = initial velocity
a = acceleration
s = distance

For the first part of the motion (penetrating the block):
0 = (V/2)^2 + 2a(4)
0 = V^2/4 + 8a

For the second part of the motion (penetrating further):
0 = (V/2)^2 + 2a(x)
0 = V^2/4 + 2ax

Subtracting the first equation from the second equation:
0 = 2ax - 8a
8a = 2ax
x = 4 cm

Therefore, the body will penetrate an additional 4 cm before coming to rest.

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